Tree-Grass interactions dynamics and Pulse Fires: mathematical and numerical studies

TL;DR

This paper models savanna tree-grass interactions using impulsive differential equations to analyze how fire regimes and shading influence vegetation dynamics across different climatic zones.

Contribution

It introduces a novel impulsive differential equation framework to study fire effects and shading in savanna ecosystems, revealing diverse vegetation outcomes.

Findings

Multiple stable states identified for vegetation composition.

Fire periodicity can cause abrupt shifts in vegetation.

Shading influences bifurcation points in vegetation dynamics.

Abstract

Savannas are dynamical systems where grasses and trees can either dominate or coexist. Fires are known to be central in the functioning of the savanna biome though their characteristics are expected to vary along the rainfall gradients as observed in Sub-Saharan Africa. In this paper, we model the tree-grass dynamics using impulsive differential equations that consider fires as discrete events. This framework allows us to carry out a comprehensive qualitative mathematical analysis that revealed more diverse possible outcomes than the analogous continuous model. We investigated local and global properties of the equilibria and show that various states exist for the physiognomy of vegetation. Though several abrupt shifts between vegetation states appeared determined by fire periodicity, we showed that direct shading of grasses by trees is also an influential process embodied in the model by a competition parameter leading to bifurcations. Relying on a suitable nonstandard finite difference scheme, we carried out numerical simulations in reference to three main climatic zones as observable in Central Africa.